Is that what you were addressing when you mentioned a disregard for the 'unclean masses'? That Plato's city really doesn't have a problem with encouraging most people to lead unexamined (and so, worthless) lives? Sorry if I'm misunderstanding anything.
The 'myth of the metals' makes it quite clear that only certain people have what it takes to become philosopher-kings, and they would be in charge of the city. He says that everyone should do what they are best at; for some, it is philosophizing, for others, it is laboring.
But I don't think this directly conflicts with Socrates' statement that 'the unexamined life is not worth living', and I don't think it means that even slaves or laborers cannot lead examined lives. Everyone has the ability, maybe the need, to examine their lives critically, and to determine what it means, how they should best live, how are they to be happy, whether or not their actions are good, and so forth. In Plato's city, it's just that the chosen philosopher-kings are the ones who make this their career, as they are the most gifted, virtuous, and trained philosophers in the city; but the rest do not then lead unexamined lives...
Also, Socrates' statement can be seen as a pointed attack against Athens' honor culture, which Socrates was highly critical of. Plato's city though holds wisdom/reason as the greatest good, so Socrates' statement from the Apology
could be taken out of context when applied to Plato's just City, where reason and examination are already supposed to rule.
And when looking at the city as the soul, you could make an interpretation where the soul has certain parts (the 'tripartite' soul): the appetites, the spirited, and the rational parts...that are represented by different groups of people in the city fulfilling their function. Reason should tie them all together and direct or lead them, so that the soul can achieve harmony with truth.